{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes_classification.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    # Check if notebook is running in Google Colab\n",
    "    import google.colab\n",
    "    # Get additional files from Github\n",
    "    !wget https://raw.githubusercontent.com/krasserm/bayesian-machine-learning/dev/gaussian-processes/gaussian_processes_util.py\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian processes for classification\n",
    "\n",
    "This article gives an introduction to Gaussian processes for classification and provides a minimal implementation with NumPy. Gaussian processes for regression are covered in a [previous article](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb?flush_cache=true) and a brief recap is given in the next section.\n",
    "\n",
    "## Regression recap\n",
    "\n",
    "A Gaussian process (GP) for regression is a [random process](https://en.wikipedia.org/wiki/Stochastic_process) where any point $\\mathbf{x} \\in \\mathbb{R}^d$ is assigned a random variable $f(\\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$ is itself Gaussian:\n",
    "\n",
    "$$\n",
    "p(\\mathbf{f} \\mid \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\mid \\boldsymbol\\mu, \\mathbf{K})\n",
    "\\tag{1}\n",
    "$$\n",
    "\n",
    "A GP is a prior over functions whose shape (smoothness, ...) is defined by $\\mathbf{K} = \\kappa(\\mathbf{X}, \\mathbf{X})$ where $\\kappa$ is a parameteric kernel function. It is common to set $\\boldsymbol\\mu = \\mathbf{0}$. Given observed noisy function values $\\mathbf{y}$ at points $\\mathbf{X}$ we want to predict a noise-free function value $f_*$ at point $\\mathbf{x}_*$. The joint distribution of observed values $\\mathbf{y}$ and prediction $f_*$ is also a Gaussian:\n",
    "\n",
    "$$\n",
    "p(\\mathbf{y}, f_* \\mid \\mathbf{X},\\mathbf{x}_*) = \n",
    "\\mathcal{N} \\left(\n",
    "\\begin{pmatrix}\\mathbf{y} \\\\ f_*\\end{pmatrix} \\middle| \\ \\boldsymbol{0},\n",
    "\\begin{pmatrix}\\mathbf{K}_y & \\mathbf{k}_* \\\\ \\mathbf{k}_*^T & k_{**}\\end{pmatrix}\n",
    "\\right)\n",
    "\\tag{2}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{K}_y = \\mathbf{K} + \\sigma_y^2\\mathbf{I}$, $\\mathbf{k}_* = \\kappa(\\mathbf{X},\\mathbf{x}_*)$ and $k_{**} = \\kappa(\\mathbf{x}_*,\\mathbf{x}_*)$. $\\sigma_y^2$ models noise in the observed function values $\\mathbf{y}$. Turning the joint distribution $(2)$ into a conditional distribution we obtain a predictive distribution\n",
    "\n",
    "$$\n",
    "p(f_* \\mid \\mathbf{x}_*, \\mathbf{X}, \\mathbf{y}) = \\mathcal{N}(f_* \\mid \\boldsymbol\\mu_*, \\boldsymbol\\Sigma_*)\n",
    "\\tag{3}\n",
    "$$\n",
    "\n",
    "with\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\boldsymbol{\\mu_*} &= \\mathbf{k}_*^T \\mathbf{K}_y^{-1} \\mathbf{y}\\tag{4} \\\\\n",
    "\\boldsymbol{\\Sigma_*} &= k_{**} - \\mathbf{k}_*^T \\mathbf{K}_y^{-1} \\mathbf{k}_*\\tag{5}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "In contrast to the notation in the [previous article](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb?flush_cache=true), I'm using here a single test input $\\mathbf{x}_*$ to be consistent with the notation in the following sections. However, the implementation further below is vectorized so that predictions can be made for multiple test inputs $\\mathbf{X}_*$ in a single operation.\n",
    "\n",
    "\n",
    "## Binary classification\n",
    "\n",
    "In context of binary classification, we have a discrete target variable $t \\in \\{0, 1 \\}$ that follows a Bernoulli distribution. We are interested in the probability $p(t=1 \\mid a) = \\sigma(a)$ where $\\sigma$ is the logistic sigmoid function taking logit $a \\in \\mathbb{R}$ as argument. $p(t=0 \\mid a)$ is given by $1 - p(t=1 \\mid a)$.\n",
    "\n",
    "### Predictive distribution\n",
    "\n",
    "Given observed targets $\\mathbf{t}$ at points $\\mathbf{X}$, our goal is to predict target $t_*$ at point $\\mathbf{x}_*$ using the predictive distribution $p(t_*=1 \\mid \\mathbf{x}_*, \\mathbf{X}, \\mathbf{t})$. Making the conditioning on input variables implicit, the notation of the predictive distribution simplifies to $p(t_*=1 \\mid \\mathbf{t})$.\n",
    "\n",
    "In the following, I will only outline the high-level steps needed to derive an expression for the predictive distribution and only present those results that are relevant for a minimal implementation. A detailed derivation of these results is given in \\[1\\], \\[2\\] and \\[3\\]. The predictive distribution can be defined as:\n",
    "\n",
    "$$\n",
    "p(t_*=1 \\mid \\mathbf{t}) = \\int{p(t_*=1 \\mid a_*) p(a_* \\mid \\mathbf{t}) d a_*}\n",
    "\\tag{6}\n",
    "$$\n",
    "\n",
    "This integral is analytically intractable. Two approximation are needed to make it tractable. First, $p(a_* \\mid \\mathbf{t})$ must be approximated with a Gaussian distribution. Second, $p(t_*=1 \\mid a_*) = \\sigma(a_*)$ must be approximated with the inverse probit function $\\Phi(a_*)$ (see also \\[2\\] section 4.3.5). Let's start with $p(a_* \\mid \\mathbf{t})$ which can be defined as:\n",
    "\n",
    "$$\n",
    "p(a_* \\mid \\mathbf{t}) = \\int{p(a_* \\mid \\mathbf{a}) p(\\mathbf{a} \\mid \\mathbf{t}) d\\mathbf{a}}\n",
    "\\tag{7}\n",
    "$$\n",
    "\n",
    "The first term inside the integral, $p(a_* \\mid \\mathbf{a})$, is a Gaussian distribution that can be obtained using a GP for regression. The joint distribution over logits $p(\\mathbf{a}, a_* \\mid \\mathbf{X}, \\mathbf{x}_*)$ is given by Equation $(2)$ which can be turned into a conditional distribution $p(a_* \\mid \\mathbf{x}_*, \\mathbf{X}, \\mathbf{a})$ using Equation $(3)$. Making the conditioning on input variables implicit gives $p(a_* \\mid \\mathbf{a})$. Instead of $\\mathbf{K}_y$ used in Equation $(2)$ we use $\\mathbf{K}_a = \\mathbf{K} + \\sigma_a^2\\mathbf{I}$. Assuming that training data are correctly labeled, we could set noise parameter $\\sigma_a^2$ to zero but for reasons of numerical stability it is convenient to set it to a small value. Using the Laplace approximation (see \\[2\\] section 4.4), the posterior distribution $p(\\mathbf{a} \\mid \\mathbf{t})$ can be approximated with a Gaussian distribution $q(\\mathbf{a})$:\n",
    "\n",
    "$$\n",
    "q(\\mathbf{a}) = \\mathcal{N}(\\mathbf{a} \\mid \\hat{\\mathbf{a}}, \\mathbf{H}^{-1})\n",
    "\\tag{8}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{H} = \\mathbf{W} + \\mathbf{K}_a^{-1}$. $\\mathbf{W}$ is a diagonal matrix with elements $\\sigma(a_n)(1 - \\sigma(a_n))$ with $a_n$ being the elements of $\\mathbf{a}$. Written in vector notation the diagonal is $\\boldsymbol\\sigma(\\mathbf{1}-\\boldsymbol\\sigma)$. The mean $\\hat{\\mathbf{a}}$ can be obtained iteratively with the following update equation:\n",
    "\n",
    "$$\n",
    "\\mathbf{a}^{\\text{new}} = \\mathbf{K}_a (\\mathbf{I} + \\mathbf{W}\\mathbf{K}_a)^{-1}(\\mathbf{t} - \\boldsymbol\\sigma + \\mathbf{W}\\mathbf{a})\n",
    "\\tag{9}\n",
    "$$\n",
    "\n",
    "At convergence $\\hat{\\mathbf{a}} = \\mathbf{a}^{\\text{new}}$. With two Gaussians inside the integral of Equation $(7)$ the result is also a Gaussian and can be obtained analytically. The Gaussian approximation of $p(a_* \\mid \\mathbf{t})$ is therefore given by\n",
    "\n",
    "\n",
    "$$\n",
    "p(a_* \\mid \\mathbf{t}) \\approx \\mathcal{N}(a_* \\mid \\mu_{a_*}, \\sigma_{a_*}^2)\n",
    "\\tag{10}\n",
    "$$\n",
    "\n",
    "with \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mu_{a_*} &= \\mathbf{k}_*^T(\\mathbf{t} - \\boldsymbol\\sigma)\\tag{11} \\\\\n",
    "\\sigma_{a_*}^2 &= k_{**} - \\mathbf{k}_*^T (\\mathbf{W}^{-1} + \\mathbf{K}_a)^{-1} \\mathbf{k}_*\\tag{12}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Finally, we approximate $p(t_*=1 \\mid a_*)$ in Equation $(6)$ with the inverse probit function $\\Phi(a_*)$ so that the predictive distribution can be approximated with:\n",
    "\n",
    "$$\n",
    "p(t_*=1 \\mid \\mathbf{t}) \\approx \\sigma(\\mu_{a_*} (1 + \\pi\\sigma_{a_*}^2 / 8)^{-1/2})\n",
    "\\tag{13}\n",
    "$$\n",
    "\n",
    "See \\[2\\] section 4.5.2 for further details about the probit approximation.\n",
    "\n",
    "### Kernel parameter optimization\n",
    "\n",
    "Kernel parameters $\\boldsymbol\\theta$ can be optimized by maximizing the log marginal likelihood log $p(\\mathbf{t} \\mid \\boldsymbol\\theta)$. Using again the Laplace approximation $q(\\mathbf{a})$ for posterior $p(\\mathbf{a} \\mid \\mathbf{t})$ the log marginal likelihood can be approximated with:\n",
    "\n",
    "$$\n",
    "p(\\mathbf{t} \\mid \\boldsymbol\\theta) \\approx \n",
    "\\mathbf{t}^T \\hat{\\mathbf{a}}\n",
    "-\\frac{1}{2} \\hat{\\mathbf{a}}^T \\mathbf{K}_a^{-1} \\hat{\\mathbf{a}}\n",
    "-\\frac{1}{2} \\log \\begin{vmatrix}\\mathbf{K}_a\\end{vmatrix}\n",
    "-\\frac{1}{2} \\log \\begin{vmatrix}\\mathbf{W} + \\mathbf{K}_a^{-1}\\end{vmatrix}\n",
    "- \\sum_{n=1}^{N} \\log(1 + e^{\\hat{a}_n})\n",
    "\\tag{14}\n",
    "$$\n",
    "\n",
    "where $N$ is the size of the training dataset. Since $\\hat{\\mathbf{a}}$ also depends on $\\boldsymbol\\theta$, $\\hat{\\mathbf{a}}$ must be re-estimated using Equation $(9)$ at each optimization step.\n",
    "\n",
    "## Multi-class classification\n",
    "\n",
    "For multi-class classification one option is to use several binary one-versus-rest classifiers. This approach, for example, is taken by [`GaussianProcessClassifier`](https://scikit-learn.org/stable/modules/generated/sklearn.gaussian_process.GaussianProcessClassifier.html) of scikit-learn and can also be applied to the implementation presented here. An extension to true multi-class classification is also possible <sup>[1],[3]</sup> but not covered in this article.\n",
    "\n",
    "## Implementation with Numpy\n",
    "\n",
    "This is the minimum we need to know for implementing GPs for binary classification. The following implementation vectorizes the computation of $p(t_*=1 \\mid \\mathbf{t})$ so that we can make predictions at multiple test inputs `X_test` in a single operation. The results are compared with those of `GaussianProcessClassifier`. The implementation presented here directly follows the definition of equations which works quite well for many cases. Numerically more stable implementation options are described in \\[1\\] and \\[3\\]. These have also been used for `GaussianProcessClassifier`, for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "from scipy.stats import bernoulli\n",
    "from scipy.special import expit as sigmoid\n",
    "\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.gaussian_process import GaussianProcessClassifier\n",
    "from sklearn.gaussian_process.kernels import ConstantKernel, RBF\n",
    "\n",
    "from gaussian_processes_util import (\n",
    "    plot_data_1D,\n",
    "    plot_data_2D,\n",
    "    plot_pt_2D,\n",
    "    plot_db_2D)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1D dataset\n",
    "\n",
    "Let's start with a simple 1D training dataset where logits $\\mathbf{a}$ are given by a sine function. Target values $\\mathbf{t}$ are sampled from a corresponding Bernoulli distribution. In the following we still assume that training data are correctly labeled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "X = np.arange(0, 5, 0.2).reshape(-1, 1)\n",
    "X_test = np.arange(-2, 7, 0.1).reshape(-1, 1)\n",
    "\n",
    "a = np.sin(X * np.pi * 0.5) * 2\n",
    "t = bernoulli.rvs(sigmoid(a))\n",
    "\n",
    "plot_data_1D(X, t)\n",
    "plt.title('1D training dataset')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$t$')\n",
    "plt.yticks([0, 1])\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training\n",
    "\n",
    "As in [Gaussian processes](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb?flush_cache=true) for regression, we again use a squared exponential kernel with length parameter `theta[0]` and multiplicative constant `theta[1]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kernel(X1, X2, theta):\n",
    "    \"\"\"\n",
    "    Isotropic squared exponential kernel.\n",
    "\n",
    "    Args:\n",
    "        X1: Array of m points (m x d).\n",
    "        X2: Array of n points (n x d).\n",
    "        theta: Kernel parameters\n",
    "\n",
    "    Returns:\n",
    "        (m x n) matrix\n",
    "    \"\"\"\n",
    "\n",
    "    sqdist = np.sum(X1 ** 2, 1).reshape(-1, 1) + np.sum(X2 ** 2, 1) - 2 * np.dot(X1, X2.T)\n",
    "    return theta[1] ** 2 * np.exp(-0.5 / theta[0] ** 2 * sqdist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helpers `K_` and `W_` ease the computation of matrices $\\mathbf{K} + \\nu \\mathbf{I}$ and $\\mathbf{W}$, respectively ($\\nu$ is set to a small value for numerical stability). `K_` also provides an efficient implementation for computing the diagonal (needed when making predictions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def K_(X, theta, diag_only=False, nu=1e-5):\n",
    "    \"\"\"Helper to apply kernel function.\"\"\"\n",
    "    if diag_only:\n",
    "        # Specific solution for isotropic \n",
    "        # squared exponential kernel.\n",
    "        return theta[1] ** 2 + nu\n",
    "    else:\n",
    "        return kernel(X, X, theta) + nu * np.eye(X.shape[0])\n",
    "\n",
    "def W_(a):\n",
    "    \"\"\"Helper to compute matrix W.\"\"\"\n",
    "    r = sigmoid(a) * (1 - sigmoid(a))\n",
    "    return np.diag(r.ravel())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function `posterior_mode` implements update Equation $(9)$ and returns the mode $\\hat{\\mathbf{a}}$ of posterior $p(\\mathbf{a}|\\mathbf{t})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior_mode(X, t, K_a, max_iter=10, tol=1e-9):\n",
    "    \"\"\"\n",
    "    Computes the mode of posterior p(a|t).\n",
    "    \"\"\"\n",
    "    a_h = np.zeros_like(t)\n",
    "    I = np.eye(X.shape[0])\n",
    "\n",
    "    for i in range(max_iter):\n",
    "        W = W_(a_h)\n",
    "        Q_inv = np.linalg.inv(I + W @ K_a)\n",
    "        a_h_new = (K_a @ Q_inv).dot(t - sigmoid(a_h) + W.dot(a_h))\n",
    "        a_h_diff = np.abs(a_h_new - a_h)\n",
    "        a_h = a_h_new\n",
    "\n",
    "        if not np.any(a_h_diff > tol):\n",
    "            break\n",
    "\n",
    "    return a_h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`nll_fn` returns the negative log likelihood function for data `X` and `t`. The returned function implements approximation $(14)$ and is a function of kernel parameters `theta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nll_fn(X, t):\n",
    "    \"\"\"\n",
    "    Returns the negative log-likelihood function for data X, t.\n",
    "    \"\"\"\n",
    "    \n",
    "    t = t.ravel()\n",
    "\n",
    "    def nll(theta):\n",
    "        K_a = K_(X, theta)\n",
    "        K_a_inv = np.linalg.inv(K_a)\n",
    "\n",
    "        # posterior mode depends on theta (via K)\n",
    "        a_h = posterior_mode(X, t, K_a).ravel()\n",
    "        W = W_(a_h)\n",
    "\n",
    "        ll = - 0.5 * a_h.T.dot(K_a_inv).dot(a_h) \\\n",
    "             - 0.5 * np.linalg.slogdet(K_a)[1] \\\n",
    "             - 0.5 * np.linalg.slogdet(W + K_a_inv)[1] \\\n",
    "             + t.dot(a_h) - np.sum(np.log(1.0 + np.exp(a_h)))\n",
    "\n",
    "        return -ll\n",
    "\n",
    "    return nll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal values for kernel parameters are obtained by minimizing the negative log marginal likelihood of the training data with `scipy.optimize.minimize`, starting from initial kernel parameter values `[1, 1]`. We let `minimize` estimate the gradients of the negative log marginal likelihood instead of computing them analytically. In the following I'll refer to the negative log marginal likelihood simply as *negative log likelihood*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized theta = [0.715, 0.836], negative log likelihood = 17.002\n"
     ]
    }
   ],
   "source": [
    "res = minimize(nll_fn(X, t), [1, 1],\n",
    "               bounds=((1e-3, None), (1e-3, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "theta = res.x\n",
    "\n",
    "print(f'Optimized theta = [{theta[0]:.3f}, {theta[1]:.3f}], negative log likelihood = {res.fun:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`predict_pt` implements approximation $(13)$ and computes class 1 probablities at inputs `X_test` given training data `X` and `t`. `predict_a` implements approximation $(10)$ and computes the mean $\\mu_{a_*}$ and variance $\\sigma^2_{a_*}$ of logits at inputs `X_test`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_a(X_test, X, t, theta):\n",
    "    \"\"\"\n",
    "    Computes the mean and variance of logits at points X_test\n",
    "    given training data X, t and kernel parameters theta.\n",
    "    \"\"\"\n",
    "    K_a = K_(X, theta)\n",
    "    K_s = kernel(X, X_test, theta)\n",
    "    a_h = posterior_mode(X, t, K_a)\n",
    "\n",
    "    W_inv = np.linalg.inv(W_(a_h))\n",
    "    R_inv = np.linalg.inv(W_inv + K_a)\n",
    "\n",
    "    a_test_mu = K_s.T.dot(t - sigmoid(a_h))\n",
    "    # Compute variances only (= diagonal) instead of full covariance matrix\n",
    "    a_test_var = K_(X_test, theta, diag_only=True) - np.sum((R_inv @ K_s) * K_s, axis=0).reshape(-1, 1)\n",
    "\n",
    "    return a_test_mu, a_test_var\n",
    "\n",
    "\n",
    "def predict_pt(X_test, X, t, theta):\n",
    "    \"\"\"\n",
    "    Computes the probability of t=1 at points X_test\n",
    "    given training data X, t and kernel parameters theta.\n",
    "    \"\"\"\n",
    "    a_mu, a_var = predict_a(X_test, X, t, theta)\n",
    "    kappa = 1.0 / np.sqrt(1.0 + np.pi * a_var / 8)\n",
    "    return sigmoid(kappa * a_mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing class 1 probabilities at `X_test` gives the following output (green line), shown in context of the training data. The black dotted line represents the decision boundary at $p(t_*=1 \\mid \\mathbf{t}) = 0.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_test = predict_pt(X_test, X, t, theta)\n",
    "\n",
    "plot_data_1D(X, t)\n",
    "plt.plot(X_test, pt_test, label='Prediction', color='green')\n",
    "plt.axhline(0.5, X_test.min(), X_test.max(), color='black', ls='--', lw=0.5)\n",
    "plt.title('Predicted class 1 probabilities')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$p(t_*=1|\\mathbf{t})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the logit variances returned by `predict_a` to estimate the uncertainty of predictions. Uncertainty increases in regions with little or no training data as can bee seen in the following plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_test_mu, a_test_var = predict_a(X_test, X, t, theta)\n",
    "\n",
    "a_test_mu = a_test_mu.ravel()\n",
    "a_test_var = a_test_var.ravel()\n",
    "\n",
    "plt.plot(X_test, a_test_mu, label='logits mean $\\mu_{a_*}$', color='green', alpha=0.3)\n",
    "plt.fill_between(X_test.ravel(), \n",
    "                 a_test_mu + a_test_var, \n",
    "                 a_test_mu - a_test_var, \n",
    "                 label='logits variance $\\sigma^2_{a_*}$', \n",
    "                 color='lightcyan')\n",
    "plt.xlabel('$x$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison with `GaussianProcessClassifier`\n",
    "\n",
    "A comparison with the results obtained by fitting a `GaussianProcessClassifier` (GPC) shows they are identical (or very close). This is the case for the optimized kernel parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized theta = [0.715, 0.836], negative log likelihood = 17.002\n"
     ]
    }
   ],
   "source": [
    "rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)\n",
    "gpc = GaussianProcessClassifier(kernel=rbf)\n",
    "\n",
    "gpc.fit(X, t.ravel())\n",
    "\n",
    "# Obtain optimized kernel parameters\n",
    "sklearn_theta_0 = gpc.kernel_.k2.get_params()['length_scale']\n",
    "sklearn_theta_1 = np.sqrt(gpc.kernel_.k1.get_params()['constant_value'])\n",
    "\n",
    "sklearn_theta_0, sklearn_theta_1, -gpc.log_marginal_likelihood_value_\n",
    "print(f'Optimized theta = [{sklearn_theta_0:.3f}, {sklearn_theta_1:.3f}], negative log likelihood = {-gpc.log_marginal_likelihood_value_:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as well as for the predicted class 1 probabilities. Minor differences mainly arise from the fact that `GaussianProcessClassifier` uses a numerically more stable implementation and that it computes the gradients of the log likelihood analytically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_test_gpc = gpc.predict_proba(X_test.reshape(-1, 1))[:,1]\n",
    "\n",
    "plot_data_1D(X, t)\n",
    "plt.plot(X_test, pt_test, label='Prediction', color='green')\n",
    "plt.plot(X_test, pt_test_gpc, label='Prediction (GPC)', color='black', ls=':')\n",
    "plt.title('Comparison with GaussianProcessClassifier (GPC)')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('$p(t_*=1|\\mathbf{t})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2D example\n",
    "\n",
    "The minimal implementation can also be used for higher-dimensional input data. Let's use [make_moons](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html) to generate a 2D training dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, t = make_moons(200, noise=0.5, random_state=1)\n",
    "t = t.reshape(-1, 1)\n",
    "\n",
    "plot_data_2D(X, t)\n",
    "plt.title('2D training dataset')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimized kernel parameters are obtained by minimizing the negative log likelihood of the new training dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized theta = [1.347, 3.362], negative log likelihood = 93.434\n"
     ]
    }
   ],
   "source": [
    "res = minimize(nll_fn(X, t), [1, 1],\n",
    "               bounds=((1e-3, None), (1e-3, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "theta = res.x\n",
    "\n",
    "print(f'Optimized theta = [{theta[0]:.3f}, {theta[1]:.3f}], negative log likelihood = {res.fun:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, a comparison with `GaussianProcessClassifier` shows that optimization results are very close."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized theta = [1.346, 3.360], negative log likelihood = 93.434\n"
     ]
    }
   ],
   "source": [
    "rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)\n",
    "gpc = GaussianProcessClassifier(kernel=rbf)\n",
    "\n",
    "gpc.fit(X, t.ravel())\n",
    "\n",
    "# Obtain optimized kernel parameters\n",
    "sklearn_theta_0 = gpc.kernel_.k2.get_params()['length_scale']\n",
    "sklearn_theta_1 = np.sqrt(gpc.kernel_.k1.get_params()['constant_value'])\n",
    "\n",
    "print(f'Optimized theta = [{sklearn_theta_0:.3f}, {sklearn_theta_1:.3f}], negative log likelihood = {-gpc.log_marginal_likelihood_value_:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is also the case for the predicted class 1 probabilities shown in the following contour plots. The black dashed line represents the decision boundary at $p(t_*=1 \\mid \\mathbf{t}) = 0.5$. The results obtained with the minimal implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_x, grid_y = np.mgrid[-4:4:200j, -4:4:200j]\n",
    "grid = np.stack([grid_x, grid_y], axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_test = predict_pt(grid.reshape(-1, 2), X, t, theta).reshape(*grid_x.shape)\n",
    "\n",
    "plt.figure(figsize=(9, 7))\n",
    "plot_pt_2D(grid_x, grid_y, pt_test)\n",
    "plot_db_2D(grid_x, grid_y, pt_test, decision_boundary=0.5)\n",
    "plot_data_2D(X, t)\n",
    "plt.title('Predicted class 1 probabilities')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "are almost identical with the results obtained with a `GaussianProcessClassifier`. A quantive evaluation of the differences is omitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_test_gpc = gpc.predict_proba(grid.reshape(-1, 2))[:, 1].reshape(*grid_x.shape)\n",
    "\n",
    "plt.figure(figsize=(9, 7))\n",
    "plot_pt_2D(grid_x, grid_y, pt_test_gpc)\n",
    "plot_db_2D(grid_x, grid_y, pt_test_gpc, decision_boundary=0.5)\n",
    "plot_data_2D(X, t)\n",
    "plt.title('Predicted class 1 probabilities (GPC)')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can again use the logit variances returned by `predict_a` as a measure of model uncertainty or (inverse) model confidence. The model is more confident within the training data region than outside this region. When moving along the decision boundary (dashed black line) the predicted class 1 probability is always 0.5 but with varying confidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_test_var = predict_a(grid.reshape(-1, 2), X, t, theta)[1].reshape(*grid_x.shape)\n",
    "\n",
    "plt.figure(figsize=(9, 7))\n",
    "plt.contourf(grid_x, grid_y, a_test_var, alpha=0.3, cmap='plasma', levels=np.linspace(0, 15, 11))\n",
    "plt.colorbar()\n",
    "plot_db_2D(grid_x, grid_y, pt_test, decision_boundary=0.5)\n",
    "plot_data_2D(X, t)\n",
    "plt.title('Uncertainty')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "\\[1\\] Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapter 15.  \n",
    "\\[2\\] Christopher M. Bishop. [Pattern Recognition and Machine Learning](https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf), Chapter 6.  \n",
    "\\[3\\] Carl Edward Rasmussen and Christopher K. I. Williams. [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/).  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
